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Proof step 13 from proof abs-erase-emptyq (previous step)

# vols[v] = # avols[v], apebs[vols[v][m, unmapped][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m < # avols[v], m0 < # avols[v], v ∈ avols, v ∈ vols, ∀ m. m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ m0 = m, (vols[v][m0] = unmapped → ¬ avols[v][m, erased][m0].mapped?) ∧ (vols[v][m, unmapped][m0] ≠ unmapped → avols[v][m0].mapped? ∧ avols[v][m0].data = buf ∧ m1 ≤ avols[v][m0].fill)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# vols[v] = # avols[v], apebs[vols[v][m0].pnum] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # avols[v], m < # avols[v], v ∈ vols, v ∈ avols, ∀ m. m < # avols[v] → (vols[v][m] = unmapped → ¬ avols[v][m].mapped?) ∧ (vols[v][m] ≠ unmapped → avols[v][m].mapped? ∧ avols[v][m].data = apebs[vols[v][m].pnum].data ∧ apebs[vols[v][m].pnum].fill ≤ avols[v][m].fill) ∧ (avols[v][m] = erased → ¬ v × m ∈ q) ⊦ m0 = m, (vols[v][m0] = unmapped → ¬ avols[v][m0].mapped?) ∧ (vols[v][m0] ≠ unmapped → avols[v][m0].mapped? ∧ avols[v][m0].data = buf ∧ m1 ≤ avols[v][m0].fill)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≠ n → evol[n, leb][m] = evol[m]; (s)% ⊦ m ≠ n → ebatbl[n, ebae][m] = ebatbl[m]; (s)